| 1 | !> @file diffusion_v.f90 |
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| 2 | !------------------------------------------------------------------------------! |
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| 3 | ! This file is part of PALM. |
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| 4 | ! |
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| 5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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| 6 | ! terms of the GNU General Public License as published by the Free Software |
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| 7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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| 8 | ! version. |
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| 9 | ! |
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| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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| 17 | ! Copyright 1997-2017 Leibniz Universitaet Hannover |
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| 18 | !------------------------------------------------------------------------------! |
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| 19 | ! |
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| 20 | ! Current revisions: |
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| 21 | ! ----------------- |
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| 22 | ! |
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| 23 | ! |
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| 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: diffusion_v.f90 2119 2017-01-17 16:51:50Z hoffmann $ |
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| 27 | ! |
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| 28 | ! 2118 2017-01-17 16:38:49Z raasch |
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| 29 | ! OpenACC version of subroutine removed |
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| 30 | ! |
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| 31 | ! 2037 2016-10-26 11:15:40Z knoop |
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| 32 | ! Anelastic approximation implemented |
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| 33 | ! |
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| 34 | ! 2000 2016-08-20 18:09:15Z knoop |
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| 35 | ! Forced header and separation lines into 80 columns |
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| 36 | ! |
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| 37 | ! 1873 2016-04-18 14:50:06Z maronga |
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| 38 | ! Module renamed (removed _mod) |
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| 39 | ! |
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| 40 | ! 1850 2016-04-08 13:29:27Z maronga |
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| 41 | ! Module renamed |
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| 42 | ! |
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| 43 | ! 1740 2016-01-13 08:19:40Z raasch |
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| 44 | ! unnecessary calculations of kmzm and kmzp in wall bounded parts removed |
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| 45 | ! |
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| 46 | ! 1682 2015-10-07 23:56:08Z knoop |
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| 47 | ! Code annotations made doxygen readable |
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| 48 | ! |
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| 49 | ! 1340 2014-03-25 19:45:13Z kanani |
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| 50 | ! REAL constants defined as wp-kind |
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| 51 | ! |
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| 52 | ! 1320 2014-03-20 08:40:49Z raasch |
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| 53 | ! ONLY-attribute added to USE-statements, |
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| 54 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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| 55 | ! kinds are defined in new module kinds, |
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| 56 | ! revision history before 2012 removed, |
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| 57 | ! comment fields (!:) to be used for variable explanations added to |
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| 58 | ! all variable declaration statements |
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| 59 | ! |
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| 60 | ! 1257 2013-11-08 15:18:40Z raasch |
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| 61 | ! openacc loop and loop vector clauses removed, declare create moved after |
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| 62 | ! the FORTRAN declaration statement |
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| 63 | ! |
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| 64 | ! 1128 2013-04-12 06:19:32Z raasch |
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| 65 | ! loop index bounds in accelerator version replaced by i_left, i_right, j_south, |
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| 66 | ! j_north |
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| 67 | ! |
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| 68 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 69 | ! code put under GPL (PALM 3.9) |
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| 70 | ! |
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| 71 | ! 1015 2012-09-27 09:23:24Z raasch |
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| 72 | ! accelerator version (*_acc) added |
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| 73 | ! |
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| 74 | ! 1001 2012-09-13 14:08:46Z raasch |
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| 75 | ! arrays comunicated by module instead of parameter list |
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| 76 | ! |
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| 77 | ! 978 2012-08-09 08:28:32Z fricke |
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| 78 | ! outflow damping layer removed |
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| 79 | ! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp |
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| 80 | ! |
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| 81 | ! Revision 1.1 1997/09/12 06:24:01 raasch |
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| 82 | ! Initial revision |
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| 83 | ! |
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| 84 | ! |
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| 85 | ! Description: |
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| 86 | ! ------------ |
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| 87 | !> Diffusion term of the v-component |
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| 88 | !------------------------------------------------------------------------------! |
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| 89 | MODULE diffusion_v_mod |
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| 90 | |
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| 91 | |
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| 92 | USE wall_fluxes_mod |
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| 93 | |
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| 94 | PRIVATE |
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| 95 | PUBLIC diffusion_v |
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| 96 | |
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| 97 | INTERFACE diffusion_v |
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| 98 | MODULE PROCEDURE diffusion_v |
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| 99 | MODULE PROCEDURE diffusion_v_ij |
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| 100 | END INTERFACE diffusion_v |
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| 101 | |
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| 102 | CONTAINS |
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| 103 | |
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| 104 | |
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| 105 | !------------------------------------------------------------------------------! |
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| 106 | ! Description: |
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| 107 | ! ------------ |
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| 108 | !> Call for all grid points |
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| 109 | !------------------------------------------------------------------------------! |
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| 110 | SUBROUTINE diffusion_v |
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| 111 | |
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| 112 | USE arrays_3d, & |
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| 113 | ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w, & |
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| 114 | drho_air, rho_air_zw |
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| 115 | |
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| 116 | USE control_parameters, & |
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| 117 | ONLY: constant_top_momentumflux, topography, use_surface_fluxes, & |
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| 118 | use_top_fluxes |
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| 119 | |
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| 120 | USE grid_variables, & |
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| 121 | ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v |
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| 122 | |
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| 123 | USE indices, & |
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| 124 | ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzb_diff_v, nzb_v_inner, & |
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| 125 | nzb_v_outer, nzt, nzt_diff |
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| 126 | |
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| 127 | USE kinds |
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| 128 | |
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| 129 | IMPLICIT NONE |
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| 130 | |
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| 131 | INTEGER(iwp) :: i !< |
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| 132 | INTEGER(iwp) :: j !< |
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| 133 | INTEGER(iwp) :: k !< |
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| 134 | REAL(wp) :: kmxm !< |
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| 135 | REAL(wp) :: kmxp !< |
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| 136 | REAL(wp) :: kmzm !< |
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| 137 | REAL(wp) :: kmzp !< |
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| 138 | |
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| 139 | REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !< |
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| 140 | |
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| 141 | ! |
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| 142 | !-- First calculate horizontal momentum flux v'u' at vertical walls, |
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| 143 | !-- if neccessary |
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| 144 | IF ( topography /= 'flat' ) THEN |
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| 145 | CALL wall_fluxes( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, nzb_v_inner, & |
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| 146 | nzb_v_outer, wall_v ) |
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| 147 | ENDIF |
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| 148 | |
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| 149 | DO i = nxl, nxr |
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| 150 | DO j = nysv, nyn |
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| 151 | ! |
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| 152 | !-- Compute horizontal diffusion |
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| 153 | DO k = nzb_v_outer(j,i)+1, nzt |
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| 154 | ! |
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| 155 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 156 | kmxp = 0.25_wp * & |
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| 157 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 158 | kmxm = 0.25_wp * & |
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| 159 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 160 | |
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| 161 | tend(k,j,i) = tend(k,j,i) & |
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| 162 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 163 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 164 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 165 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 166 | & ) * ddx & |
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| 167 | & + 2.0_wp * ( & |
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| 168 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 169 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 170 | & ) * ddy2 |
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| 171 | ENDDO |
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| 172 | |
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| 173 | ! |
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| 174 | !-- Wall functions at the left and right walls, respectively |
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| 175 | IF ( wall_v(j,i) /= 0.0_wp ) THEN |
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| 176 | |
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| 177 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
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| 178 | kmxp = 0.25_wp * & |
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| 179 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 180 | kmxm = 0.25_wp * & |
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| 181 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 182 | |
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| 183 | tend(k,j,i) = tend(k,j,i) & |
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| 184 | + 2.0_wp * ( & |
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| 185 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 186 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 187 | ) * ddy2 & |
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| 188 | + ( fxp(j,i) * ( & |
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| 189 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 190 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 191 | ) & |
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| 192 | - fxm(j,i) * ( & |
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| 193 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 194 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 195 | ) & |
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| 196 | + wall_v(j,i) * vsus(k,j,i) & |
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| 197 | ) * ddx |
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| 198 | ENDDO |
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| 199 | ENDIF |
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| 200 | |
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| 201 | ! |
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| 202 | !-- Compute vertical diffusion. In case of simulating a Prandtl |
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| 203 | !-- layer, index k starts at nzb_v_inner+2. |
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| 204 | DO k = nzb_diff_v(j,i), nzt_diff |
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| 205 | ! |
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| 206 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 207 | kmzp = 0.25_wp * & |
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| 208 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 209 | kmzm = 0.25_wp * & |
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| 210 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 211 | |
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| 212 | tend(k,j,i) = tend(k,j,i) & |
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| 213 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 214 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 215 | & ) * rho_air_zw(k) & |
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| 216 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 217 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 218 | & ) * rho_air_zw(k-1) & |
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| 219 | & ) * ddzw(k) * drho_air(k) |
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| 220 | ENDDO |
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| 221 | |
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| 222 | ! |
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| 223 | !-- Vertical diffusion at the first grid point above the surface, |
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| 224 | !-- if the momentum flux at the bottom is given by the Prandtl law |
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| 225 | !-- or if it is prescribed by the user. |
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| 226 | !-- Difference quotient of the momentum flux is not formed over |
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| 227 | !-- half of the grid spacing (2.0*ddzw(k)) any more, since the |
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| 228 | !-- comparison with other (LES) models showed that the values of |
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| 229 | !-- the momentum flux becomes too large in this case. |
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| 230 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 231 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 232 | IF ( use_surface_fluxes ) THEN |
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| 233 | k = nzb_v_inner(j,i)+1 |
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| 234 | ! |
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| 235 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 236 | kmzp = 0.25_wp * & |
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| 237 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 238 | |
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| 239 | tend(k,j,i) = tend(k,j,i) & |
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| 240 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 241 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 242 | & ) * rho_air_zw(k) & |
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| 243 | & - ( -vsws(j,i) ) & |
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| 244 | & ) * ddzw(k) * drho_air(k) |
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| 245 | ENDIF |
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| 246 | |
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| 247 | ! |
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| 248 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 249 | !-- if the momentum flux at the top is prescribed by the user |
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| 250 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 251 | k = nzt |
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| 252 | ! |
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| 253 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 254 | kmzm = 0.25_wp * & |
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| 255 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 256 | |
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| 257 | tend(k,j,i) = tend(k,j,i) & |
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| 258 | & + ( ( -vswst(j,i) ) & |
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| 259 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 260 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 261 | & ) * rho_air_zw(k-1) & |
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| 262 | & ) * ddzw(k) * drho_air(k) |
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| 263 | ENDIF |
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| 264 | |
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| 265 | ENDDO |
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| 266 | ENDDO |
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| 267 | |
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| 268 | END SUBROUTINE diffusion_v |
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| 269 | |
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| 270 | |
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| 271 | !------------------------------------------------------------------------------! |
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| 272 | ! Description: |
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| 273 | ! ------------ |
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| 274 | !> Call for grid point i,j |
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| 275 | !------------------------------------------------------------------------------! |
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| 276 | SUBROUTINE diffusion_v_ij( i, j ) |
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| 277 | |
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| 278 | USE arrays_3d, & |
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| 279 | ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w, & |
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| 280 | drho_air, rho_air_zw |
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| 281 | |
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| 282 | USE control_parameters, & |
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| 283 | ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes |
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| 284 | |
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| 285 | USE grid_variables, & |
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| 286 | ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v |
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| 287 | |
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| 288 | USE indices, & |
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| 289 | ONLY: nzb, nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff |
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| 290 | |
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| 291 | USE kinds |
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| 292 | |
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| 293 | IMPLICIT NONE |
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| 294 | |
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| 295 | INTEGER(iwp) :: i !< |
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| 296 | INTEGER(iwp) :: j !< |
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| 297 | INTEGER(iwp) :: k !< |
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| 298 | REAL(wp) :: kmxm !< |
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| 299 | REAL(wp) :: kmxp !< |
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| 300 | REAL(wp) :: kmzm !< |
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| 301 | REAL(wp) :: kmzp !< |
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| 302 | |
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| 303 | REAL(wp), DIMENSION(nzb:nzt+1) :: vsus !< |
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| 304 | |
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| 305 | ! |
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| 306 | !-- Compute horizontal diffusion |
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| 307 | DO k = nzb_v_outer(j,i)+1, nzt |
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| 308 | ! |
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| 309 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 310 | kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 311 | kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 312 | |
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| 313 | tend(k,j,i) = tend(k,j,i) & |
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| 314 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 315 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 316 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 317 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 318 | & ) * ddx & |
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| 319 | & + 2.0_wp * ( & |
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| 320 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 321 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 322 | & ) * ddy2 |
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| 323 | ENDDO |
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| 324 | |
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| 325 | ! |
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| 326 | !-- Wall functions at the left and right walls, respectively |
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| 327 | IF ( wall_v(j,i) /= 0.0_wp ) THEN |
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| 328 | |
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| 329 | ! |
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| 330 | !-- Calculate the horizontal momentum flux v'u' |
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| 331 | CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), & |
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| 332 | vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp ) |
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| 333 | |
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| 334 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
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| 335 | kmxp = 0.25_wp * & |
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| 336 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 337 | kmxm = 0.25_wp * & |
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| 338 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 339 | |
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| 340 | tend(k,j,i) = tend(k,j,i) & |
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| 341 | + 2.0_wp * ( & |
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| 342 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 343 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 344 | ) * ddy2 & |
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| 345 | + ( fxp(j,i) * ( & |
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| 346 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 347 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 348 | ) & |
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| 349 | - fxm(j,i) * ( & |
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| 350 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 351 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 352 | ) & |
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| 353 | + wall_v(j,i) * vsus(k) & |
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| 354 | ) * ddx |
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| 355 | ENDDO |
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| 356 | ENDIF |
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| 357 | |
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| 358 | ! |
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| 359 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 360 | !-- index k starts at nzb_v_inner+2. |
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| 361 | DO k = nzb_diff_v(j,i), nzt_diff |
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| 362 | ! |
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| 363 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 364 | kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 365 | kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 366 | |
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| 367 | tend(k,j,i) = tend(k,j,i) & |
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| 368 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 369 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 370 | & ) * rho_air_zw(k) & |
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| 371 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 372 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 373 | & ) * rho_air_zw(k-1) & |
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| 374 | & ) * ddzw(k) * drho_air(k) |
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| 375 | ENDDO |
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| 376 | |
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| 377 | ! |
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| 378 | !-- Vertical diffusion at the first grid point above the surface, if the |
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| 379 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
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| 380 | !-- prescribed by the user. |
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| 381 | !-- Difference quotient of the momentum flux is not formed over half of |
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| 382 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
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| 383 | !-- other (LES) models showed that the values of the momentum flux becomes |
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| 384 | !-- too large in this case. |
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| 385 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 386 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 387 | IF ( use_surface_fluxes ) THEN |
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| 388 | k = nzb_v_inner(j,i)+1 |
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| 389 | ! |
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| 390 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 391 | kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 392 | |
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| 393 | tend(k,j,i) = tend(k,j,i) & |
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| 394 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 395 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 396 | & ) * rho_air_zw(k) & |
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| 397 | & - ( -vsws(j,i) ) & |
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| 398 | & ) * ddzw(k) * drho_air(k) |
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| 399 | ENDIF |
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| 400 | |
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| 401 | ! |
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| 402 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 403 | !-- if the momentum flux at the top is prescribed by the user |
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| 404 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 405 | k = nzt |
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| 406 | ! |
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| 407 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 408 | kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 409 | |
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| 410 | tend(k,j,i) = tend(k,j,i) & |
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| 411 | & + ( ( -vswst(j,i) ) & |
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| 412 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 413 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 414 | & ) * rho_air_zw(k-1) & |
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| 415 | & ) * ddzw(k) * drho_air(k) |
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| 416 | ENDIF |
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| 417 | |
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| 418 | END SUBROUTINE diffusion_v_ij |
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| 419 | |
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| 420 | END MODULE diffusion_v_mod |
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